I'll make some assumptions in fill in the needed information, but feel free to correct it.
1) you have 6 minnows in a 240 gallon tank. I assume they are each around 2.5" for this discussion. That's a total of 11 grams of fish. Assuming they are also fed (also not mentioned) at 3% body weight per day, with 35% protein 90% dry weight food, that would generate ~ 0.05 ppm nitrates per day.
2) you are adding market shrimp each week. There was no mention of how many or what size, so I'll assume 2 per week, at around 11 grams in size each. Shrimp are ~83% protein and 59% water, so that works out to ~3.8 ppm of nitrate per week.
So that works out in total to ~4 ppm nitrates per week. Since you are doing water changes (of an unstated amount), you will indeed have virtually no nitrates after 6 weeks.
Your readings on ammonia and nitrite probably depend on when you take them. If its within 24 hours of the shrimp being fed they could be high. At any other time it would generate negligible readings. I calculate 0.01 ppm of ammonia and 0.04 ppm of nitrite.
In the linked thread on fishless cycling, it's recommded that one add 5 drops of ammonia (.41 grams) for every 10 gallons of water each day. In a 240 gallon tank, that would be 9.6 grams per day on average. By my estimates above, you are adding .3 grams per day.
According to my assumptions (again, they are merely assumptions) you have inadequate imput. My guess it that most of the original bacteria has been lost, but that's again, an assumption.